Question

A rectangle is three times as long as it is wide. The perimeter is $36\text{in}$ What is the length of each side?

Answer 1

Step-1: Find the width of rectangle:

Given: Perimeter $=36\text{in}$ and rectangle is three times as long as it is wide

Let width $w$ of the rectangle be $\mathrm{x}\text{in}$

Then its length $l=3\mathrm{x}\text{in}$

So Perimeter of rectangle $=2\left(l+w\right)$

$\Rightarrow$ $36=2\left(3\mathrm{x}+\mathrm{x}\right)$

$\Rightarrow$ $36=2\left(4\mathrm{x}\right)$

$\Rightarrow$ $36=8\mathrm{x}$

$\Rightarrow$ $4.5\text{in}=\mathrm{x}$

Step-2: Find the length of rectangle:

As the length of rectangle $=3\mathrm{x}\text{in}$

So, length $=3\times 4.5$

$\Rightarrow$ $=13.5\text{in}$

Hence, length and width of the rectangle are $13.5\text{in}$ and $4.5\text{in}$ respectively.